Only a few hours into his trip to the U.K., Britons learned that the American president who had just shaken up NATO allies in Brussels was not out of the provocation business.

Around the time a dinner in Mr. Trump’s honor was taking place at an Oxfordshire palace, word spread that he had given an interview highly critical of the dinner’s host. That would be Prime Minister Theresa May.

And so ended Day 1.

Some highlights of the trip so far:

• Mr. Trump, fresh from breaking eggs in Brussels, was back in form in Britain, telling a newspaper that Prime Minister May was mishandling the Brexit talks.

• Shortly after he arrived at the ambassador’s residence and again outside the dinner, protesters began to make their voices heard.

Well, this should be an interesting lunch

Near the end of the gala dinner Mrs. May was hosting for Mr. Trump on Thursday night, word emerged that he had given a newspaper interview in which he criticized her handling of the Brexit negotiations and appeared to boost the fortunes of a political rival.

If Mrs. May persists in seeking a so-called soft exit from the European Union, Mr. Trump reportedly told The Sun, she can forget about a separate pact with the United States. He described her approach as “very unfortunate.”

“If they do that,” the paper quoted him as saying, “then their trade deal with the U.S. will probably not be made.”

He had much warmer words for Boris Johnson, the ambitious British politician who just quit as foreign minister in an open break with May.

Mr. Johnson, he said, would “make a great prime minister.”

The bombshell interview may give Mr. Trump and Mrs. May something to talk about on Friday — when they are to meet for lunch.

The dinner itself was closed to the press, but shortly before 8 p.m., Mr. and Ms. Trump arrived at the place and were greeted by Mrs. May and her husband, Philip.

The Mays emerged from the palace — a hulking, yellow-tinged stone building with Corinthian columns, ornate turrets and statues adorning the top — and strode down red-carpeted steps and across a large cobblestone plaza.

A band wearing black pants, red coats with gold detail and black furry hats was assembled on both sides of the red carpet, and a crowd of black tie-clad people were in front of the palace awaiting the president’s arrival.

Outside the palace gates, the mood was less celebratory. Hundreds of protesters held signs protesting Mr. Trump’s visit. Many carried signs that read “No to Racism, No to Trump.” The demonstration was peaceful, and photos posted to social media showed families with young children gathered on the streets of the Oxfordshire town.

(Stephen Castle and Kimiko de Freytas-Tamura, look to Trump’s visit to Britain, explain why the American president’s visit could be an ordeal more than anything else, despite the “special relationship.”)

Protesters across from the ambassador’s residence, where the Trumps were staying the night, unleashed a “wall of sound.” It featured the cries of children detained by U.S. immigration authorities, as well a relentless stream of slogans, whistles and the banging of pots and drums.

As the presidential helicopter descended on the grounds of the ambassador’s residence in Regent’s Park, preparing to whisk Mr. Trump away to a black-tie dinner in a secluded palace outside the capital, protesters raised a cry.

British authorities had set up a metallic cage around the ambassador’s residence, where President Trump is staying overnight, as part of his security.

On Thursday, activists gave a taste of the protests planned on Friday, though the crowd thinned out after the president left for the dinner at Blenheim Palace.

Organizers hope to mount the biggest weekday demonstration in Britain since protests against the Iraq War more than a decade ago.

“He needs to be called out,” said Harley Day, 23, a college student who joined the protest after classes. “His bigotry, his sexism, his Islamophobia, his general xenophobia and crass inability to empathize.”

Mr. Trump strongly recommitted American support for NATO, a bedrock of Western security policy for generations, on Thursday, comments that at least temporarily calmed fears that he might move toward dismantling the alliance.

“The United States commitment to NATO is very strong, remains very strong,” he said at a news conference in Brussels. “I believe in NATO.”

But if Mr. Trump’s public remarks were friendly, the tone behind closed doors was much harsher. Officials from other countries voiced fears that even if he had not broken an alliance that was first formed in 1949 to contain the Soviet Union, he had thrown some sand in its gears.

Mr. Trump insisted that despite his criticism of the alliance and some of its member countries, there was no animosity in private meetings with other leaders.

“There’s a great, very collegial spirit in that room,” he said. “Very unified, very strong, no problem”

According to a person briefed on Mr. Trump’s meeting with other NATO leaders, Mr. Trump said that if the other countries did not increase military spending to 2 percent of their economic output by January, the United States “would go it alone.”

What that would mean was not clear to the officials who were present. White House officials did not immediately respond to requests to explain Mr. Trump’s comment, or to say whether he was suggesting that the United States could withdraw from NATO.

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The French president, Emmanuel Macron, dismissed such concerns as unfounded.

“Generally I do not comment on what goes on behind the scenes, but at no moment did President Trump — neither bilaterally nor multilaterally — say that he was intending to leave NATO,” Mr. Macron said.

Mr. Trump has not held a news conference on American soil for more than a year. But on Thursday, flanked by Secretary of State Mike Pompeo and John R. Bolton, his national security adviser, he took questions from reporters for over a half an hour.

He dismissed any concern that his relationship with Russia was too cozy or that his relationship with allies was too harsh. — Katie Rogers, Julie Hirschfeld Davis and Steven Erlanger

Did NATO agree to spending increases? 2 European leaders say no.

President Emmanuel Macron of France contradicted President Trump on Thursday, saying that NATO members had simply confirmed a 2014 commitment to increase military spending to 2 percent of gross domestic product by 2024.Credit
Francois Mori/Associated Press

Mr. Trump said that other NATO countries had agreed to significant increases in military spending in response to his demands.

But within a few hours, Emmanuel Macron, the French president, and Giuseppe Conte, Italy’s prime minister, said the allies had simply agreed to keep a 2014 commitment to increase military spending to 2 percent of gross domestic product by 2024.

Mr. Conte said: “Italy inherited spending commitments to NATO, commitments that we did not change, so no increase in spending. As far as we’re concerned, today we did not decide to offer extra contributions with respect to what was decided some time ago.”

Angela Merkel, the German chancellor, said that her country would consider more spending, but said nothing about making any new commitments. And she undercut the notion that reconsideration of Germany’s defense budget was due simply to American pressure.

“Given the discussion of many European allies here, not just the American discussion, I think we have to ask again and again what else can we possibly do,” she said.

Mr. Trump has insisted that NATO countries meet the 2 percent threshold right away, and that the long-term target be doubled to 4 percent.

“The additional money that they’re willing to put up has been really amazing,” Mr. Trump said, without addressing amounts or a timetable. “Yesterday I let them know that I was extremely unhappy with what was happening, and they have substantially upped their commitment.”

Mr. Trump once again hailed himself as a “very stable genius” and took “total credit” for persuading his allies to increase military spending. And he took credit for other NATO countries having increased their military spending by $33 billion in the last year.

“I don‘t think that’s helping Russia,” he said. “I think NATO is much stronger now than it was two days ago.”

As the leaders walked to the site of a group photograph, many of them chatting easily with one another, Mr. Trump hung back, with the president of Turkey, Recep Tayyip Erdogan.

When they took their assigned spots, Mr. Trump stood near the center, but his counterparts mostly ignored him, giving him no more than sidelong glances, even as several of them continued conversing.

A number of news organizations noted the awkwardness, drawing rebukes from White House aides, who called it “fake news.”

Fake News Media outlets FAIL to mention the photo of President @realDonaldTrump looking up toward the sky with others, is that of an impressive flyover of helicopters from 13 Alied Nations as seen here off the reflection of the @NATO building. Way to go FAKE NEWS! pic.twitter.com/OV7EX857AK

Hours after Mr. Trump castigated Germany, he met with Chancellor Angela Merkel, then the two of them briefed reporters on their conversation. The president smiled and spoke of a “very, very good relationship;” the chancellor did not. — Katie Rogers

On military spending, Trump cites a real imbalance in misleading ways

United States soldiers during a military exercise with allied troops in Poland in June.Credit
Laetitia Vancon for The New York Times

American presidents have long pressed their NATO counterparts to increase military spending. But Mr. Trump’s insistence that the other nations owe money misstates how the alliance works, and the figures he cites are misleading.

NATO has a budget to cover shared costs and some equipment used in joint operations, and all 29 member countries contribute to it. None of the allies has failed to pay its contribution.

Mr. Trump’s complaint is that, while NATO member countries have agreed to spend at least 2 percent of their gross domestic products on military spending, most do not. But none has violated that agreement, because the 2 percent figure is a target to be reached by 2024.

According to NATO, all members have significantly raised military spending since 2014, and eight are expected to meet the goal this year.

Mr. Trump tweeted on Monday that the United States accounted for 90 percent of military spending by NATO countries, but the alliance says the real figure is about 67 percent. And most American military spending is not NATO-related.

Even so, the organization says on its website, “There is an overreliance by the alliance as a whole on the United States for the provision of essential capabilities, including, for instance, in regard to intelligence, surveillance and reconnaissance; air-to-air refueling; ballistic missile defense; and airborne electronic warfare.”

— Julie Hirschfeld Davis and Steven Erlanger

Wrapping up the trip: One on one with Putin

Mr. Trump’s meeting with President Vladimir V. Putin of Russia, center, will be closely analyzed for signs of whether the American leader is friendlier to his Russian counterpart than he is to leaders of countries that have traditionally been allies.Credit
Pool photo by Alexei Nikolsky

Mr. Trump’s first summit meeting with the Russian president will be parsed for countless layers of meaning.

The West’s stance toward Russia is, as always, a central topic at the NATO meeting, and the United States’ European allies are worried that Mr. Trump aims to reduce the American security role in dealing with Moscow.

Mr. Trump’s 2016 campaign is under investigation for links to Russia, and Mr. Trump, who is quick to aim a barb at almost anyone else, has been reluctant to criticize Mr. Putin. Yet he and his aides bristle at accusations that he is not tough enough with the Kremlin.

The meeting with Mr. Putin will be closely analyzed for signs that Mr. Trump is friendlier to his Russian counterpart than to the leaders he is meeting in Brussels.

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